---- > [!definition] Definition. ([[positive matrix]]) > A [[matrix]] over $\mathbb{R}$ or $\mathbb{C}$ is called **positive** if all of its elements are real and positive. > [!warning] Warning. > This concept is unrelated to that of [[positive semidefinite matrix|positive semidefinite]] or [[positive definite matrix|positive definite matrices]]. > [!basicproperties] > - If $A$ is positive, then the [[network|directed graph]] for which it is the [[adjacency matrix]] is fully-connected ([[number of walks of given length on a network|1-step between any node pair]].) > - The converse is false! Take $A=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}.$ ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```